The Feller property on Riemannian manifolds

The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or C 0 -diffusion property). Both parabolicity and stochastic completeness have been the subject of a syst...

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Bibliographic Details
Published inJournal of functional analysis Vol. 262; no. 5; pp. 2481 - 2515
Main Authors Pigola, Stefano, Setti, Alberto G.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2012
Subjects
Comparison results
Feller property
Riemannian manifolds
Comparison results
Riemannian manifolds
Feller property
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Summary:The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or C 0 -diffusion property). Both parabolicity and stochastic completeness have been the subject of a systematic study which led to discovering not only sharp geometric conditions for their validity but also an incredible rich family of tools, techniques and equivalent concepts ranging from maximum principles at infinity, function theoretic tests (Khasʼminskii criterion), comparison techniques etc. The present paper aims to move a number of steps forward in the development of a similar apparatus for the Feller property.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2011.12.001